Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916703262212096 |
|---|---|
| author | Tominec, Igor Ahlkrona, Josefin Braack, Malte |
| author_facet | Tominec, Igor Ahlkrona, Josefin Braack, Malte |
| contents | This paper shows that the Stokes problem is well-posed when velocity and pressure simultaneously vanish on the domain boundary. This result is achieved by extending Nečas' inequality to square-integrable functions that vanish in a small band covering the boundary. It is found that the associated a priori pressure estimate depends inversely on the volume of the band. Numerical experiments confirm these findings. Based on these results, guidelines are provided for applying vanishing pressure boundary conditions in model coupling and domain decomposition methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions Tominec, Igor Ahlkrona, Josefin Braack, Malte Numerical Analysis Analysis of PDEs 65N12, 65N30, 65J20 This paper shows that the Stokes problem is well-posed when velocity and pressure simultaneously vanish on the domain boundary. This result is achieved by extending Nečas' inequality to square-integrable functions that vanish in a small band covering the boundary. It is found that the associated a priori pressure estimate depends inversely on the volume of the band. Numerical experiments confirm these findings. Based on these results, guidelines are provided for applying vanishing pressure boundary conditions in model coupling and domain decomposition methods. |
| title | Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions |
| topic | Numerical Analysis Analysis of PDEs 65N12, 65N30, 65J20 |
| url | https://arxiv.org/abs/2407.15971 |